Question: Simplify the following expression: $\sqrt{175} - \sqrt{7}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{175} - \sqrt{7}$ $= \sqrt{25 \cdot 7} - \sqrt{7}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{7} - \sqrt{7}$ $= 5\sqrt{7} - \sqrt{7}$ Finally, simplify by combining the terms. $= ( 5 - 1 )\sqrt{7} = 4\sqrt{7}$